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Center for Nonlinear Studies |
We introduce a new shock-capturing technique for solving nonlinear conservation laws. The method consists of adding a nonlinear viscosity to the Galerkin formulation of the nonlinear equation or system of equations. The key idea is that the added nonlinear viscosity is proportional to the residual of the entropy equation and is always limited by first-oder dissipation. The method is very simple to implement with various discretizations: finite elements, spectral elements, and Fourier approximation. We can prove that it is convergent in some simple scalar cases, and test the performance of the method numerically on various two-dimensional benchmarks from scalar equations and nonlinear systems of conservation laws.
Host: Mikhail Shashkov